DATA ON THE CRYSTAL GROWTH OF CALCITE FROM CALCIUM 

BICARBONATE SOLUTIONS AT 34°C AND CO2 PARTIAL 

PRESSURES OF 0.101, 0.0156 AND 0.00102 ATMOSPHERES

By L. Niel Plummer and Eurybiades Busenberg

Open-File Report 99-247

Reston, Virginia 

1999
U.S. Department of the Interior

BRUCE BABBITT, Secretary

U.S. Geological Survey

Charles G. Groat, Director

The use of firm, trade, and brand names in this report is for identification purposes only 

and does not constitute endorsement by the U.S. Geological Survey.

For Additional information write to:

Chief, Branch of Regional Research

Eastern Region

U.S. Geological Survey

432 National Center

12201 Sunrise Valley Drive

Reston, Virginia 20192

Copies of this report can be purchased 

from:

U.S. Geological Survey 

Branch of Information Services 

Box 25286 

Denver, CO 80225-0286
CONTENTS

Abstract.......................................................................................................................... 1

Introduction .................................................................................................................... 1

Description of crystal growth experiments......................................................................!

Results of experiments.................................................................................................... 2

Rate models and near-equilibrium rates...........................................................................6

Conclusion .....................................................................................................................12

References cited .............................................................................................................12

ILLUSTRATIONS

1. Laboratory rates as a function of calcite saturation index ........................................ 5

2. Log rate as a function of calcite saturation index ..................................................... 7

3. Comparison of calcite dissolution and crystal growth rates .................................... 10

4. Rate of calcite growth as a function of the CaHCCh activity product.................... 11

TABLE

1. Laboratory results for calcite crystal growth, 34 °C ................................................... 3

CONVERSION FACTORS

Temperature can be converted to degrees Celsius (°C) or degrees Fahrenheit (°F) 

by the following equations:

°C = (°F-32)/1.8 

°F = (1.8x°C) + 32

in
DATA ON THE CRYSTAL GROWTH OF CALCITE FROM 

CALCIUM BICARBONATE SOLUTIONS AT 34°C AND CO2 

PARTIAL PRESSURES OF 0.101, 0.0156 AND 0.00102 

ATMOSPHERES

By L. Niel Plummer and Eurybiades Busenberg

ABSTRACT

Calcite crystal growth was studied in the laboratory by determining the weight gain of 

single crystals of Iceland spar in Ca-HCOs solutions at 34 °C and CC>2 partial pressures of 

0.101, 0.0156 and 0.00102 atm, and calcite saturation indices of 0.2 to 1.9. At constant 

CC>2 partial pressure, PCOZ, and temperature, the rate of crystal growth varied linearly with 

the activity product of Ca2+ and HCOs" in solution. At constant saturation state, growth 

rate was nearly independent of Pco2 between 0.00102 and 0.0156 atm, but increased at 

the highest PCOZ- The maximum calcite growth rate was 25,000 mm/ka at SIC=1.6 and 

PCOZ of 0.101 atm. Growth rate decreased with decreasing saturation state, but rates less 

than 100 mm/ka could not be reliably measured by the laboratory weight-gain method. 

Near-equilibrium laboratory rates of calcite dissolution and crystal growth in "clean" Casolutions decrease abruptly, and remain very small over the range of Sic = 0 ± 0.2.

INTRODUCTION

The kinetics of calcite dissolution and crystal growth have been extensively studied in the 

laboratory (see for example, Nancollas and Reddy, 1971; Sjoberg, 1978; Morse, 1978; 

Plummer and others, 1978, 1979; Reddy and others, 1981; Morse, 1983; Sjoberg and 

Rickard, 1984; Inskeep and Bloom, 1985; Busenberg and Plummer, 1986; Chou and 

others, 1989; Compton and Unwin , 1990; Compton and Pritchard, 1990; Wollast, 1990; 

Morse and Mackenzie, 1990; Svensson and Dreybrodt, 1992; Van Cappellen and others, 

1993; Arakaki and Mucci, 1995; and references therein). The study described here builds 

on the earlier work of Busenberg and Plummer (1986) in which rates of dissolution and 

crystal growth of calcite were measured by change in weight of single crystals of Iceland 

spar calcite after contact with aqueous calcium bicarbonate solutions.

DESCRIPTION OF CRYSTAL GROWTH EXPERIMENTS

Supersaturated solutions of calcium bicarbonate were prepared by dissolving calcite in 

CO2-saturated water at approximately 4 °C. The solution was filtered and stored in 

refrigerated, sealed glass containers until used (see Reddy and others, 1981 for further 

details). The solution was analyzed by EDTA titration (Plummer and Busenberg, 1982), 

diluted to the desired range, placed in a stirred, constant temperature reaction vessel at 34 

°C, and equilibrated with a CO2-N2 gas mixture by continuous bubbling. Three gas 

mixtures were used 10.1, 1.56, and 0.102 percent CC>2. The partial pressure of CC>2 in 

the reaction solution was calculated by assuming that the total pressure of the CO2-N2 gas 

mixture plus saturated water vapor was equal to the room barometric pressure (Plummer 

1
and Busenberg, 1982; Busenberg and Plummer, 1986).

Single crystals of calcite were prepared from rhombohedral cleavage fragments of 

Iceland spar with total surface areas of 3 to 6 cm2 . Each crystal was tied with fine Pt-Ir 

wire with a small loop used to suspend the crystal in aqueous solutions. Surface area was 

calculated from the measured dimensions of the rhomboid faces. The crystals were 

reacted initially with IN HC1, washed with de-ionized water, dried, tied with the Pt-Ir 

wire, reacted with 0. IN HC1 for approximately 30 seconds, washed with de-ionized 

water, and dried overnight in an oven at 80 °C. The crystals, tied with Pt-Ir wire, were 

weighed on a Mettler electronic balance (Model ME22-BA25-BE22) to the nearest ug, 

recording room barometric pressure, temperature, and relative humidity. Each weight 

was corrected to in vacuo. All weights were reproducible within 2 u,g or less.

The single crystals of calcite were suspended in the supersaturated calcium bicarbonate 

solutions. Many of the measurements were made in duplicate, that is, two crystals were 

suspended in the same reaction vessel. Measurements made in duplicate are identified in 

Table 1 as pairs of experiments with identical run times and solution composition. The 

experimental design constitutes a nearly constant-composition system, as the amounts of 

calcite formed were usually less than 1 mg from solution volumes of approximately 500 

ml. Rates were determined by weight gain of the single crystals reacted over periods of 

approximately 20 to nearly 400 minutes. Further details of the experimental procedures 

are given in Busenberg and Plummer (1986). The experimental conditions and rates of 

the 91 measurements at calcite saturation indices of 0.15 to 1.87 are summarized in Table 

1.

RESULTS OF EXPERIMENTS

Laboratory measurements of calcite growth were used to determine the dependence of 

growth rate in calcium bicarbonate solutions to variations in CC>2 partial pressure and 

calcite saturation state at 34 °C as equilibrium is approached. Three CC>2 partial pressures 

were used in the experiments (10.1, 1.56 and 0.102 % CC>2 in N2). Table 1 summarizes 

the solution compositions, saturation states with respect to calcite, masses of calcite 

grown, and growth rates. Crystal surface area ranged from 3.4 to 6.6 cm2 and averaged 

4.3 cm2 . Reaction times were typically 20 to 60 minutes. The calcite saturation index 

ranged from 0.15 to 1.87, and weight gain ranged from about 0 to nearly 2000 u,g. Three 

crystals actually lost weight (runs 28, 33, and 103; of 2, 9, and 3 u,g, respectively). 

Although this weight loss may be from physical loss of solid from the samples prior to 

weighing, both runs involving weight loss occurred nearest equilibrium for reactions in 

0.102 and 10.1 % CC>2. However, these observations were not reproducible (see run 34, 

Table 1, which was a duplicate of run 33) and are likely due to sample damage.

Maximum rates of approximately 25,000 mm/ka were obtained from calcite growth at 

saturation indices of about 1.6 in calcium bicarbonate solutions saturated with 10.1 % 

CC>2. Figure 1 shows that at constant saturation state, calcite growth rate decreases with 

decreasing CC>2 partial pressure in calcium bicarbonate solutions, but the rate dependence 

on PCo2 is relatively small at CO2 partial pressures in the range of 1.56% CC>2 and lower. 

2
Table 1: Laboratory results of calcite crystal growth, 34 °C

[Ca, Calcium; mmol/kg, millimoles per kilogram of water; Calc., Calculated; pH, -log activity of hydrogen 

ion; IAP, Ion Activity Product of CaCO3 ; p, -log activity; H, hydrogen ion; CO3 , carbonate ion; HCO3 , 

bicarbonate ion; cm , square centimeters; Min., minutes; mg, milligrams; mg/cm /sec, milligrams per 

centimeter squared per second; mm/ka, millimeters per 1000 years, SI, Saturation Index of calcite = log 

IAP/K, where K is the calcite equilibrium constant]

Exp. No.

69

70

13

14

75

76

40

39

60

59

61

62

53

54

45

46

21

22

36

28

7

1

6

44

43

68

67

88

87

80

79

90

89

74

73

12

11

51

52

81

82

%CO2

0.102

0.102

0.102

0.102

0.102

0.102

0.102

0.102

0.102

0.102

0.102

0.102

0.102

0.102

0.102

0.102

0.102

0.102

0.102

0.102

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

Ca 

mmol 

/kg

2.66

2.66

2.42

2.42

2.12

2.12

1.89

1.89

1.84

1.84

1.74

1.74

1.65

1.65

1.43

1.43

1.34

1.34

1.19

0.98

8.81

8.81

8.81

5.93

5.93

5.77

5.77

5.58

5.58

5.45

5.45

5.25

5.25

5.12

5.12

5.04

5.04

4.99

4.99

4.95

4.95

Calc. 

pH

8.52

8.52

8.48

8.48

8.44

8.44

8.39

8.39

8.39

8.39

8.37

8.37

8.34

8.34

8.29

8.29

8.26

8.26

8.22

8.14

7.81

7.84

7.84

7.70

7.70

7.69

7.69

7.68

7.68

7.67

7.67

7.65

7.65

7.65

7.65

7.64

7.64

7.63

7.63

7.63

7.63

-Log 

IAP

6.92

6.92

7.02

7.02

7.15

7.15

7.27

7.27

7.30

7.30

7.36

7.36

7.42

7.42

7.57

7.57

7.65

7.65

7.77

8.00

6.66

6.66

6.66

7.07

7.07

7.10

7.10

7.14

7.14

7.16

7.16

7.20

7.20

7.23

7.23

7.25

7.25

7.26

7.26

7.27

7.27

pCa

2.79

2.79

2.82

2.82

2.86

2.86

2.90

2.90

2.91

2.91

2.93

2.93

2.95

2.95

2.99

2.99

3.02

3.02

3.06

3.13

2.38

2.38

2.38

2.50

2.50

2.50

2.50

2.51

2.51

2.52

2.52

2.53

2.53

2.54

2.54

2.55

2.55

2.55

2.55

2.55

2.55

pC03

4.13

4.13

4.20

4.20

4.29

4.29

4.37

4.37

4.39

4.39

4.43

4.43

4.47

4.47

4.58

4.58

4.63

4.63

4.72

4.87

4.28

4.28

4.28

4.58

4.58

4.60

4.60

4.62

4.62

4.64

4.64

4.67

4.67

4.69

4.69

4.70

4.70

4.71

4.71

4.72

4.72

pHCO3

2.39

2.39

2.42

2.42

2.46

2.46

2.51

2.51

2.52

2.52

2.54

2.54

2.56

2.56

2.61

2.61

2.63

2.63

2.68

2.76

1.87

1.87

1.87

2.02

2.02

2.03

2.03

2.04

2.04

2.05

2.05

2.06

2.06

2.07

2.07

2.08

2.08

2.08

2.08

2.08

2.08

Area 

cm

5.56

4.42

4.00

4.01

4.22

4.05

4.92

5.56

4.22

3.77

4.19

4.05

4.32

5.20

4.22

4.05

4.00

4.01

3.77

3.36

3.81

5.20

4.00

3.36

4.22

5.20

4.32

4.92

6.56

5.20

4.32

4.01

4.00

3.77

4.19

4.92

5.56

5.56

4.92

4.19

3.77

Time 

Min.

22

22

35

35

20

20

51

51

20

20

20

20

50

50

64

64

53

53

237

58

12

22

22

41

41

20

20

21

21

20

20

20

20

20

20

35

35

51

51

23

23

Wt. 

Gain 

mg

0.735

0.463

0.783

0.755

0.313

0.245

0.858

1.182

0.184

0.212

0.188

0.223

0.418

0.501

0.355

0.273

0.253

0.256

0.51

-0.002

0.107

1.023

0.783

0.979

1.15

0.834

0.848

0.332

0.481

0.435

0.383

0.263

0.257

0.423

0.43

0.570

0.887

1.69

1.308

0.251

0.205

RatelO5 

mg/cm2/ 

sec

10.01

7.94

9.32

8.97

6.18

5.04

5.70

6.95

3.63

4.69

3.74

4.59

3.23

3.21

2.19

1.76

1.99

2.01

0.95

-0.02

3.90

14.90

14.83

11.84

11.08

13.37

16.36

5.36

5.82

6.97

7.39

5.47

5.35

9.35

8.55

5.52

7.60

9.93

8.69

4.34

3.94

Rate 

mm/ka

11601

9193

10798

10386

7160

5840

6602

8048

4209

5428

4331

5315

3736

3720

2538

2033

2304

2326

1102

-20

4518

17265

17179

13720

12832

15482

18949

6204

6741

8075

8558

6331

6202

10831

9907

6391

8800

11507

10064

5029

4564

SI

1.62

1.62

1.52

1.52

1.39

1.39

1.26

1.26

1.24

1.24

1.18

1.18

1.12

1.12

0.97

0.97

0.89

0.89

0.76

0.54

1.87

1.87

1.87

1.46

1.46

1.44

1.44

1.40

1.40

1.37

1.37

1.33

1.33

1.31

1.31

1.29

1.29

1.28

1.28

1.27

1.27
Table 1 (continued)

Exp. No.

80

79

91

92

83

84

50

49

57

58

85

86

64

63

66

65

17

18

19

20

26

25

31

32

94

93

97

98

3

55

56

78

77

10

9

41

42

48

47

15

16

24

23

30

29

34

33

71

Ca 

% CO2 mmol/kg

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

1.56

10.1

10.1

10.1

10.1

10.1

10.1

10.1

10.1

10.1

10.1

10.1

10.1

10.1

10.1

10.1

10.1

10.1

10.1

10.1

10.1

4.94

4.94

4.84

4.84

4.40

4.40

4.20

4.20

4.09

4.09

4.04

4.04

3.95

3.95

3.83

3.83

3.73

3.73

3.03

3.03

2.44

2.44

2.14

2.14

1.99

1.99

1.83

1.83

12.94

10.46

10.46

9.50

9.50

7.97

7.97

7.48

7.48

6.78

6.78

5.77

5.77

5.00

5.00

4.37

4.37

4.10

4.10

1.09

Calc. 

pH

7.63

7.63

7.62

7.62

7.58

7.58

7.56

7.56

7.56

7.56

7.55

7.55

7.54

7.54

7.53

7.53

7.52

7.52

7.44

7.44

7.35

7.35

7.30

7.30

7.27

7.27

7.24

7.24

7.20

7.12

7.12

7.09

7.09

7.02

7.02

6.99

6.99

6.95

6.95

6.89

6.89

6.83

6.83

6.78

6.78

6.75

6.75

7.11

-Log pCa 

IAP

7.27 2.55

7.27 2.55

7.29 2.56

7.29 2.56

7.40 2.59

7.40 2.59

7.45 2.61

7.45 2.61

7.47 2.61

7.47 2.61

7.49 2.62

7.49 2.62

7.51 2.62

7.51 2.62

7.55 2.64

7.55 2.64

7.58 2.64

7.58 2.64

7.81 2.71

7.81 2.71

8.06 2.79

8.06 2.79

8.21 2.83

8.21 2.83

8.29 2.86

8.29 2.86

8.39 2.89

8.39 2.89

7.01 2.25

7.24 2.31

7.24 2.31

7.33 2.34

7.33 2.34

7.52 2".40

7.52 2.40

7.60 2.42

7.60 2.42

7.70 2.45

7.70 2.45

7.88 2.50

7.88 2.50

8.04 2.54

8.04 2.54

8.19 2.59

8.19 2.59

8.26 2.61

8.26 2.61

7.27 2.33

pC03

4.71

4.71

4.73

4.73

4.81

4.81

4.84

4.84

4.86

4.86

4.87

4.87

4.89

4.89

4.91

4.91

4.94

4.94

5.10

5.10

5.27

5.27

5.38

5.38

5.43

5.43

5.50

5.50

4.76

4.92

4.92

4.99

4.99

5.13

5.13

5.18

5.18

5.26

5.26

5.38

5.38

5.50

5.50

5.60

5.60

5.66

5.66

4.94

pHCO3 Area 

cm2

2.09

2.09

2.09

2.09

2.13

2.13

2.15

2.15

2.16

2.16

2.16

2.16

2.17

2.17

2.19

2.19

2.20

2.20

2.28

2.28

2.36

2.36

2.42

2.42

2.45

2.45

2.48

2.48

1.70

1.78

1.78

1.82

1.82

1.89

1.89

1.91

1.91

1.95

1.95

2.01

2.01

2.07

2.07

2.12

2.12

2.15

2.15

1.80

4.09

3.81

4.22

3.36

4.22

3.36

4.09

3.81

4.32

5.20

3.81

4.09

3.36

4.22

4.09

3.81

4.22

4.05

5.56

4.92

4.05

4.22

5.20

5.56

5.20

4.32

4.09

4.92

5.56

4.00

4.01

3.36

4.22

5.20

4.32

4.00

4.01

3.77

4.19

4.19

3.77

5.20

4.32

3.77

4.19

4.01

4.92

4.00

Time 

Min.

20

20

20

20

20

20

61

61

20

20

22

22

20

20

21

21

49

49

52

55

62

62

387

387

125

125

99

99

20

49

49

20

20

40

40

51

51

65

65

49

49

55

55

66

66

386

386

17

Wt. Rate'105 

Gain mg/cm2/ Rate 

mg sec mm/ka

0.427

0.481

0.295

0.216

0.174

0.126

0.781

0.879

0.176

0.223

0.177

0.173

0.124

0.149

0.183

0.184

0.236

0.183

0.240

0.168

0.041

0.05

0.218

0.242

0.022

0.017

0.012

0.023

1.484

1.931

1.984

0.565

0.641

1.023

0.761

0.717

0.718

0.617

0.595

0.256

0.132

0.296

0.229

0.029

0.056

0.017

-0.009

0.482

8.70

10.52

5.83

5.36

3.44

3.13

5.22

6.30

3.40

3.57

3.52

3.20

3.08

2.94

3.55

3.83

1.90

1.54

1.38

1.03

0.27

0.32

0.18

0.19

0.06

0.05

0.05

0.08

22.24

16.42

16.83

14.01

12.66

8.20

7.34

5.86

5.85

4.20

3.64

2.08

1.19

1.72

1.61

0.19

0.34

0.02

-0.01

11.81

10078

12187

6748

6206

3980

3620

6044

7302

3933

4140

4077

3712

3563

3408

4114

4440

2203

1780

1603

1199

315

369

209

217

65

61

57

91

25765

19021

19494

16233

14663

9496

8503

6786

6778

4861

4218

2407

1380

1998

1861

225

391

21

-9

13685

SI

1.27

1.27

1.25

1.25

1.14

1.14

1.09

1.09

1.06

1.06

1.05

1.05

1.02

1.02

0.99

0.99

0.96

0.96

0.72

0.72

0.47

0.47

0.32

0.32

0.24

0.24

0.15

0.15

1.53

1.30

1.30

1.20

1.20

1.01

1.01

0.94

0.94

0.83

0.83

0.66

0.66

0.50

0.50

0.35

0.35

0.27

0.27

1.27
Table 1 (continued)

Ca

Exp. No. % CO2 mmol Calc. -Log 

/kg pH IAP

pCa pCO3 pHCO3 Area Time 

cm2 Min.

Wt. Rate'105

Gain mg/cm2/

mg sec

Rate 

mm/ka

SI

72 10.1 1.09 7.11 7.27 2.33 4.94 1.80 4.01 17 0.437 10.68 12376 1.27 

103 10.1 5.13 6.77 8.14 2.53 5.61 2.61 4.00 20 -0.003 -0.06 -72 0.40

30000 -

O 

O 

O

T-

£ 

£,

o*-»

(0 

DC

O

o

20000 -

10000-

0

34 °C

CO2 Partial Pressure (atm)

A 0.101

o 0.01 56 (Fresh)

 0.01 56 (Used)

a 0.00102

A,'

A

0,0 0.4 0.8 1.2 1.6

Calcite Saturation Index

2.0

Figure 1: Laboratory rates of calcite growth at 34 °C and COi partial pressures of 0.101, 

0.0156, and 0.00102 atmospheres, for calcite saturation indices of 0.2 to 2.0. Solid 

circles denote rates obtained from Iceland spar crystals that were re-used in successive 

growth experiments without acid washing (1,56 % COi only). The dashed lines are fits to 

the experimental data at 0.101 and 0.00102 atm.CO2 .
In other experiments, crystals that had grown previously in laboratory solutions saturated 

with 1.56 % CO2 were re-used in successive growth experiments without acid treatment. 

The previously reacted crystals (denoted "used" on Figure 1) usually grew faster than 

clean, fresh crystals by as much as a factor of 2 (Figures 1 and 2).

Using Scanning Force Microscopy, Dove and Hochella (1993) found that precipitation of 

calcite began with the formation of surface nuclei that spread and coalesced as growth 

continued, and spiral growth began only after several hours of reaction in nearequilibrium CO2 -saturated solutions. The increase in rate we observe for previously 

reacted crystals relative to fresh, unreacted crystals may be due to increase in surface area 

as the surface evolves during growth.

Uncertainties in the laboratory rates become very large below rates of 100 mm/ka. On 

the log rate scale of Figure 2, the rate curve must decrease steeply to -oo as SI calcite 

approaches 0.

RATE MODELS AND NEAR-EQUILIBRIUM RATES

Considerable progress has been made in developing mechanistic rate laws that describe 

both dissolution and growth of calcite crystals, obey the principle of microscopic 

reversibility, and predict rates under a wide range of pH, PCOZ, and calcite-saturation state 

conditions (Plummer and others, 1978, 1979; Chou and others, 1989; Van Cappellen and 

others, 1993; Zuddas and Mucci, 1994; Arakaki and Mucci, 1995).

Plummer and others (1978) studied the dissolution of calcite in the CaCO3-H2O-CO2 -HCl 

system both far from equilibrium using pH-stat methods, and as equilibrium was 

approached in "free-drift" dissolution experiments. From measurements of the forward 

rate dependence on H*, CO2(aq) and H2O, the overall net rate of reaction (positive for 

dissolution, negative for precipitation) was defined as

R =

where ki, k2 and ks are first-order rate constants for the forward reaction dependent on 

temperature, and k4 is a second-order back-reaction rate constant dependent on PCOZ and 

temperature. A theoretical expression was derived for l^by assuming that the 

composition of the fluid in the boundary layer adjacent to the crystal surface was in 

equilibrium with calcite at the bulk-fluid CO2 partial pressure. This assumption may be 

valid for relatively high CO2 partial pressures (Pco2>0.03 atm), but could fail at lower 

CO2 partial pressures if the boundary layer PC02 deviates from the bulk fluid and is a 

function of the reactant flux between the mineral surface and bulk fluid (Plummer and 

others, 1979). Theoretical values of IQ compared favorably with experimental values 

from dissolution experiments in CO2 -H2O solutions (Plummer and others, 1978). The
100000

tr ioooo-s

o 

o 

o

E 

g

0) *-»

Cw

f^" 

JC

^

o

e>

1000-s

100 i

-

A ft __

1 W Tj

2

I

-

i T

:

-

0.1 -

.' '}. £<^®

j°° 34 °C

^ A

I

i

i

CO2 Partial Pressure (atm)

A 0.101

o 0.0156 (Frash)

 0.0156 (Used)

a O.OO102 

- - -PWP (0.101)

 - PWP (0.0156)

 - .PWP (0.00102)

i | i | i | i | i

0.0 0.4 0.8 1.2 1.6

Calcite Saturation Index

2.0

Figure 2: Log rate of calcite crystal growth as a function of calcite saturation index. The 

experimental data indicate that crystal growth rates fall rapidly as equilibrium is 

approached. The dashed lines show rate calculated from the mechanistic model of 

Plummer and others (1978), PWP, which adequately describes the growth rate at SIC 

>0.4, but over-estimates rates near equilibrium.
rate expression, derived solely from dissolution data, was shown to describe calcite 

crystal growth in controlled laboratory experiments (Reddy and others, 1981; Busenberg 

and Plummer, 1986). The dashed lines on Figure 2 show rates calculated from the model 

of Plummer and others, (1978) at the 3 CO2 partial pressures used here and 34 °C. In the 

calculations, the rate constants and thermodynamic data were from Plummer and others 

(1978, 1982), except for k^ (the rate constant for the water reaction, see Plummer and 

others, 1978)) which was taken from Chou and others (1989). The laboratory rates, and 

the dependence of growth rate on Pco2 and saturation state, are adequately described by 

the Plummer and others (1978) model at calcite saturation indices above about 0.4, but 

fall below the calculated rates as equilibrium is approached at saturation indices below 

0.4 (Figure 2).

Studies by Inskeep and Bloom (1985), and Chou and others (1989) identified problems 

with the Plummer and others (1978) rate law above pH of about 8. (The experimental 

data of the present study range in pH from 7.0 to 8.5). Chou and others (1989) proposed 

dependence of the back reaction on the activity product of Ca2+ and COs2". As evidence 

for backward reaction dependence on the Ca2+ and CO32" activity product, Chou and 

others (1989) presented a non-linear relation between backward rate (obtained at variable 

Pco2) as a function of the Ca2+ HCOs" activity product, and linear dependence on the 

activity product of Ca2+ and COs2" (see Figure 4b of Chou and others, 1989). The 

comparison of Figure 4b of Chou and others (1989) is considered to be misleading, 

however, because it does not account for the Pco2 dependence o

Only one reaction is needed to describe the forward rate at low Pco2 and high pH. 

Plummer and others (1978) chose to represent the reaction with water as reactant,

2+ CaCO3 + H2O <-» Caz" + HCCV +OKT,

to maintain consistency with the predominant Ca2+ and HCCV speciation in their 

laboratory fluids. The reaction could equally have been written as

2- CaCO3 <-» Caz" + CCV'.

Because the dissociation of HCCV to CC>32~can be assumed to occur instantaneously 

during the dissolution and crystal growth of calcite, either reaction can be applied in the 

mechanistic model of Plummer and others (1978) for dilute solutions where the aH20 is 

virtually unity. The reason for this is that the forward rate is known from experiments far 

from equilibrium in compositional regions where rate is independent of Pco2 and pH. 

The principle of microscopic reversibility and data on the thermodynamic stability of 

calcite then equally define the backward reaction rate for either rate expression. As 

shown by Plummer and others (1978), the backward rate constant for the reaction of 

calcite with H2O as reactant is large at low Pco2, and thus, in principle, either reaction can 

describe the rate of backward reaction. Nevertheless, the performance of the mechanistic 

model of Plummer and others (1978) could be improved at high pH if modified to define 

more accurately the C(>2 partial pressure in the boundary layer adjacent to the mineral 

surface during reaction. 

8
Van Cappellen and others (1993) derived a surface complexation model for the chemical 

speciation at the carbonate mineral-water interface. They proposed that two species 

(>CaOH° and >CO3H°) form at hydration sites on the calcite surface when fresh calcite 

comes in contact with water. The model then predicts the development of surface charge 

and surface speciation as these sites interact with aqueous solutions. These authors 

showed that the surface-complexation model provided a framework that was capable of 

describing the pH and CO2 dependence of calcite dissolution. Arakaki and Mucci (1995) 

expanded the surface-complexation model of Van Cappellen and others (1993) to include 

both dissolution and crystal growth of calcite, incorporating aspects of the mechanistic 

models of Plummer and others (1978) and Chou and others (1989).

The mechanistic models (Plummer and others, 1978; Chou and others, 1989), and surface 

complexation models (Van Cappellen and others, 1993; Arakaki and Mucci, 1995) 

provide theoretical frameworks for describing experimental kinetic results and predicting 

rates beyond experimental conditions. Both approaches can be enhanced to account for 

inhibiting effects of foreign ions, by including additional terms to describe the effects of 

adsorption of foreign ions on rate (Busenberg and Plummer, 1986; Svensson and 

Dreybrodt, 1992), or by including reactions for the formation of additional surface 

complexes (Van Cappellen and others, 1993). Both approaches have also, with some 

success, adequately described the rates of dissolution and crystal growth of calcite in 

aqueous solutions where the driving force for reaction was relatively large. Specifically, 

these models are most reliable when applied to aqueous solutions where calcite saturation 

is approximately -0.2>SIC>0.2. But in the region near equilibrium (SIC=0±0.2), rates of 

crystal growth and dissolution are very small and not described by either the mechanistic 

model or surface-complexation approach.

Both the mechanistic and surface-complexation models overestimate the rate of 

dissolution in the sub-saturated region nearest equilibrium (-0.2>SIC>0), and overestimate 

growth rates in the over-saturated region nearest equilibrium (0.2>SIC>0). Figure 3 shows 

calcite dissolution and growth rate data from Busenberg and Plummer (1986) as a 

function of the CaHCOs activity product in calcium bicarbonate solutions saturated with 

CO2 at 25 °C and covering a range in SIC of nearly -oo to 1.0. The experimental data show 

that the measured rate in "pure" laboratory fluids plateaus in the near-equilibrium region. 

It is possible that trace impurities are still present and inhibit the laboratory rate near 

equilibrium. If this is so, then all near-equilibrium calcite rates in natural environments 

will be inhibited. It is also possible that the free energy of reaction must exceed the 

adsorption energy of water and aqueous species at the calcite surface for net reaction to 

proceed. The mechanistic model (Plummer and others, 1978) was derived from rate 

measurements at substantial under saturation where surface energies could be ignored. 

Near equilibrium, the surface energies of adsorption of water and all aqueous species, 

including adsorbed inhibitors, compete with the net reaction energy and slow the rate as 

equilibrium is approached. At present, there are no models that adequately describe both 

near and far from equilibrium the rates of calcite dissolution and crystal growth. Rates 

calculated from the models of Plummer and others (1978) and Arakaki and Mucci (1995) 

vary smoothly between the dissolution and precipitation fields, passing directly through 

9
^ 2E-006 -

o 

o

O OE+000-

E

-2E-006 -

Dissolution

s* 0 25 °C, 1 atm CO2

W

\ 5

o : 

..........Qo.

c

i

1

1

UJ

r

 >-fv

L

Zero Rate

Q

00 o

°o<^

§ 0

j^ o

2 Growth ° 0 o

0.0001 0.0002

I 

0.0003

Figure 3: Rates of dissolution and crystal growth of calcite at 25 °C in CO2-saturated 

water as a function of the CaHCOs activity product in solution (Busenberg and Plummer, 

1986). The plot shows a plateau in rate in the near-equilibrium region (SIC=0±0.17). The 

forward rate far from equilibrium occurs at 0 for the CaHCOs activity product (SIc=-°o). 

Equilibrium occurs at zero rate where the CaHCOs activity product is 0.68xlO'4 . The 

maximum CaHCOs activity product shown corresponds to a saturation index of 

approximately 1.0.

10
the point of zero rate at SIC=0, as required by microscopic reversibility. Consequently, 

these models over-estimate both rates of dissolution and crystal growth, which decrease 

abruptly and plateau near equilibrium. Calcium bicarbonate solutions saturated with COi 

were chosen to make this point in Figure 3 because the rate departures are more evident 

at high concentrations than at low concentrations. The plateau in rate near equilibrium 

occurs at all CO2 partial pressures, but is usually overlooked at low PCo2 values.

Figure 4 shows the calcite growth rates reported here at 34 °C and CO2 partial pressures 

of 0.101, 0.0156, and 0.00102 atm as a function of the calcium bicarbonate activity 

product. In all three cases, the growth rate varies linearly with the calcium bicarbonate 

activity product (at constant PCOZ), but extrapolates to zero at solution compositions that 

are slightly supersaturated with respect to calcite. Although the compositional width of 

the near-equilibrium region, where the rate plateaus, decreases with decreasing CO2 

partial pressure, the range corresponds thermodynamically to the near-equilibrium region 

of 0<SIC<0.2 in calcite saturation index (Busenberg and Plummer, 1986). Calcite 

saturation is commonly observed in the range SIC=0±0.2 in waters from limestone 

aquifers. Further work is needed to develop theoretical models of calcite dissolution and 

growth in near-equilibrium solutions.

30000

o 

o Oo 20000-

E 

E

*- 10000-

8 

O

o, 

/

34 °C

0.

^ ® '^ A Equilibrium

L ^--» 0.101 atm. 

^"^ 0.01S* atm.

0.00102 atm.

I ' I

0 4.0 8.

a v 51 V ' r! _2+ W Ouctn- * 

CO, Partial Pressure (atm)

4 0.101

o 0.0156 (Fr«sh| 

 0.0156 (Used) 

o 0.00102

 -PWP (0.0156 atm) 

 PWP(0.00102itm|

1

0 12 

I06

.0

Figure 4: Rate of calcite growth at CO2 partial pressures of 0.101, 0.0156, and 0.00102 

atm and 34°C as a function of the CaHCOj activity product in solution. The plateau in 

rate near equilibrium (also seen in Figure 3) is evident at the lower CO2 partial pressures. 

The dashed lines show rate calculated from the mechanistic model of Plummer and others 

(1978). The solid symbols at zero rate correspond to equilibrium for each CO2 partial 

pressure. Other symbols are as described in Figures 1 and 2.

11
CONCLUSION

Calcite crystal growth was studied in the laboratory by determination of weight gain of 

single crystals of Iceland spar in Ca-HCO3 solutions at 34 °C and CC>2 partial pressures of 

0.101, 0.0156 and 0.00102 atm and calcite saturation indices of 0.15 to 1.87. The rate of 

crystal growth varied linearly with the activity product of Ca2+ and HCOs" in solution. 

At constant saturation state, growth rate was nearly independent of Pco2 between 0.00102 

and 0.0156 atm, but increased at the highest PCOZ- The maximum calcite growth rate was 

25,000 mm/ka at SIc=1.6 and PCo2 of 0.101 atm. Growth rates less than 100 mm/ka 

could not be reliably measured by the laboratory weight-gain method. If not treated with 

acid between use, growth rate of individual Iceland spar crystals increased by as much as 

a factor of 2 with re-use, possibly due to increase in surface area.

At calcite saturation indices greater than 0.4, the laboratory rates of crystal growth were 

adequately described by the mechanistic model of Plummer and others (1978). The 

laboratory rates for fresh Iceland spar crystals show that growth rate is extremely 

sensitive to saturation state near equilibrium. In the near-equilibrium region of Sic = 0 ± 

0.2, rates of calcite dissolution and crystal growth are very small and are not described by 

either the mechanistic model or the surface-complexation model of calcite dissolution 

and crystal growth.

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Arakaki, T., and Mucci, A.,1995, A continuous and mechanistic representation of calcite

reaction-controlled kinetics in dilute solutions at 25 °C and 1 atm total pressure:

Aquatic Geochemistry, v. 1, p. 105-130. 

Busenberg, E., and Plummer, L.N., 1986, A comparative study of the dissolution and

crystal growth kinetics of calcite and aragonite, in Studies in Diagenesis, F.A.

Mumpton, ed.: U.S. Geological Survey Bulletin 1578, p. 139-168. 

Chou, L., Garrels, R.M., and Wollast, R., 1989, Comparative study of the kinetics and

mechanisms of dissolution of carbonate minerals: Chemical Geology, v. 78, p. 269-

282. 

Compton, R.G., and Unwin, P.R., 1990, The dissolution of calcite in aqueous solution at

pH < 4: Kinetics and mechanism: Philosophical Transactions Royal Society

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Compton, R.G., and Pritchard, K.L., 1990, The dissolution of calcite at pH > 7: Kinetics

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Dove, P.M., and Hochella, M.F., Jr= 1993, Calcite precipitation mechanisms and

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et Cosmochimica Acta, v. 49, p. 2165-2180.

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12
Morse, J.W., 1983, The kinetics of calcium carbonate dissolution and precipitation, in

Reviews in Mineralogy (v. 11), Reeder, J.R., ed.: Mineralogical Society of

America, Washington, D.C., p. 227-264. 

Morse, J.W., and Mackenzie, F.T., 1990, Geochemistry of Sedimentary Carbonates.

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dissolution in CO2-water systems at 5 to 60 ° and 0.0 to 1.0 atm CO2 : American

Journal of Science, v. 278, p. 179-216. 

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Plummer, L.N., and Busenberg, E., 1982, The solubilities of calcite, aragonite, and

vaterite in CO2-H2O solutions between 0 and 90 °C, and an evaluation of the

aqueous model for the system CaCOs-CO2 -H2O: Geochimica et Cosmochimica

Acta, v. 46, p. 1011-1040. 

Reddy, M.M., Plummer, L.N., and Busenberg, E., 1981, Crystal growth of calcite from

calcium bicarbonate solutions at constant PCOZ and 25 °C: A test of a calcite

dissolution model: Geochimica et Cosmochimica Acta, v. 45, p. 1281-1289. 

Sjoberg, E.L., 1978, Kinetics and mechanism of calcite dissolution in aqueous solutions

at low temperatures: Acta Univ. Stockholm Contrib. Geol., v. 332, p. 1-92. 

Sjoberg, E.L., and Rickard, D.T., 1984, Calcite dissolution kinetics: surface speciation

and the origin of the variable pH dependence: Chemical Geology, v. 42, p. 119-

136. 

Svensson, U., and Dreybrodt, W., 1992, Dissolution kinetics of natural calcite in CO2 -

water systems approaching calcite equilibrium: Chemical Geology, v. 100, p. 129-

145. 

Van Cappellen, P., Charlet, L., Stumm, W., and Wersin, P., 1993, A surface

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Geochimica et Cosmochimica Acta, v. 57, p. 3505-3518. 

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Natural Waters, W. Stumm, ed.: Wiley Interscience, pp. 431-445. 

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et Cosmochimica Acta, v. 58, p. 4353-4362.

13